Wireless standards are using extensively in convolutional codes. A Viterbi decoding convolutional code often forms part of common convolutional decoders. The original Viterbi process, described in the late 1960's, has been overlooked in favor of less complex Viterbi processes.
The original derivation of the Viterbi process was in the probability domain. The output of the process is a sequence of decoded bits along with corresponding reliabilities. “Soft” reliability information is described by the A Posteriori Probability (APP) (i.e., P(u|y)). For an estimate of bit u (−1/+1) having received symbol y, an optimum soft output (i.e., L(u)) is calculated according to formula 1 as follows:
                              L          ⁡                      (            u            )                          =                              ln            ⁡                          (                              P                ⁡                                  (                                      u                    =                                                                  +                        1                                            ⁢                                                                                          ⁢                      y                                                        )                                            )                                            P            ⁡                          (                              u                =                                                      -                    1                                    ⁢                                                                          ⁢                  y                                            )                                                          (        1        )            The parameter L(u) is called a Log-Likelihood Ratio (LLR). The LLR value is a convenient measure that encapsulates both soft and hard bit information in a single number. The sign of the number corresponds to the hard decision while the magnitude gives a reliability estimate.